1 Evaluate the improper intergal | dx (x2 + 9)° using the residue theorem.

Q: Calculate the third degree Taylor polynomial for y=sinh(x) around x=1 . (Hint: Use Euler s Formula)

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Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: 3. Given the ODE = 3x2- x²y ; y(2) = 5. Find the second order Taylor dy dx polynomial for y as a…

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Q: 13. Consider the integral | dx then (which statement(s) is/are correct) x2 - 4x 1 (i) -dx…

A: Given: ∫1x2-4xdx

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Jizl=1z² sinh z Where 0 < |z| < T.

A: Image is attached with detailed solution.

Q: 4- 2x Evaluate the following integral : dx 2x +4,

A: The answer is π/3.

Q: dx integralini hesaplayınız. 1-x3

A: Evaluation of integral

Q: 5. Write a 5th degree Taylor polynomial for f(x) = cos(2x) centered at x = T/4. %3D

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Q: sinz Calculate Rz-4|<T z(z-R)² dz using Residue Theorem. |z-4|<n z(z-n)²

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Q: 2. Expand the function f(x) = tan-1 x up to the first two non-zero terms in the Taylor's polyno-…

A: Solution is given below:

Q: 5. Calculate the second-degree Taylor polynomial of f(x, y) the point (1,0). tan-' (x + 2y) at %3D

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Q: a) Find the degree 3 Taylor polynomial T3 (2) for the function f(x) = 4 cos(r) centered at the point…

A: The function f(x)=4cos(x) centered at the point a=π4

Q: 1 Find the quadratic approximation of f(x) = arctan(x) at c = Round the coefficients to four . √√3…

A: The given function is           f(x)=arctan(x)=tan-1(x) To find the quadratic approximation of the…

Q: Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).

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Q: ind the Taylor polynomial of degree 2 centered at a=π that approximates f(x)=cos(5x) P2(x)=

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Q: What is the Wronskian for y" + 3y = In x? & W 3 b. W = 3 c. W = V3cos 3x-V3 sin V3x d. W 3 cos 3x -3…

A: Here, the characteristic equation is m2+3=0. So,                         m2+3=0⇒m=±3 Thus, the…

Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral:…

A: This question is based on chain rule differentiation and indefinite integral.

Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 - 10- dx 2.316 • 10-11 122-10- Using trapezoidal…

A: The solution to the integral can be calculated using numerical methods. The formula for the…

Q: 9-x2 18-x²-y² xydzdydx. B: Find the integral fo J

A: Triple integral

Q: 1. Find the maximum of the function: f (x) = 4sinx (1+ cosx ) a. Using Golden Section Search with…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: ax² + bx+c, g(x) = -ax² + bx+c, where ac # 0, th hat f(x) g(x)=0 has at least two rool roots

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Q: n for f(x) = tan(2). %3D %3D Calculate the Taylor polynomials T2(x) and T3(x) centered at a Ta(피)…

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Q: Evaluate the integral. x² - 81 | V=² x x² - 81 | Vx² x √x². 81 X √x². 81 X x² - 81 X 1² 1² - dx = -…

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Q: 2) Find the third degree Taylor polynomial centered at c= for the function. 6 f(x) = sinx

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Q: Compute dx using the techniques as presented in class and in our textbook. Show all 2x +5x-3 the…

A: we first factor the denominator

Q: Find the degree  2 Taylor polynomial T2(x) for f(x) = tan x centered at x = π/3

A: First, we will find the general Taylor series of f(x) = tan x centered at x = π/3. We know that…

Q: Find y2 using Reduction of Order xy" – 3xy' + 4y = 0 , %3D

A: Given differential equation x2y''−3xy'+4y=0....1 Given a solution y1=x2 We have to find the y2 We…

Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

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Q: (b) For f(z) find the residue of f (z) at the singular point (z+1)2(z2+4) z = -1

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Q: Find the Fourier integral of the function f(x)= e* when x> 0 and f(-x) = f(x) for k > 0 cosix and…

A: Fourier integral, for even function

Q: Find the nth Taylor polynomial centered at c. f(x) = x°cos x, n = 2, SCos C = T

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Q: 9-x2 B: Find the integral S 18-x2-y xydzdydx.

A: We have to calculate the given intregration

Q: Expand xy² + 2x – 3y in powers of (x + 2) and (y – 1) upto third degree | terms.

A: Given ,  f(x,y) = xy2 + 2x - 3y  By Taylor's theorem  f(x,y) = f(a,b) + {(x-a)fx(a,b) +…

Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: 3.2 Let f(x) = Approximate the integral x4 x L f(x) dx using the Trapezoidal rule with n = 4. -2

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Q: 1. Find the Taylor polynomial p3 centered at a = 7/3 for f(x) = = COS I.

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Q: Use Dirichlet's principle with n = 10 to find a rational approximation of T.

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Q: Evaluate the improper intergal 1 drusing the residue theorem. (x² + 16)?

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Q: Find the residue at z = 0 of the function 1 / (z + z^2)

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Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z2 sinh z Where 0 < |z| < T.

A: Use the following formulae, to evaluate the given complex integral. Let z0 be a pole of order n,…

Q: xcosr (i) Find the Cauchy principal value of the integral dr. ² + 4x + 8

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Calculate the residue of ez.z-5 at z=0

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Q: Find T3(x): the Taylor polynomial of degree 3 of the function f(x) = cos(6x) at a = 0.

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Q: dx Evaluate the integral: 3/2 64 -

A: To solve the given integral problem.

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where 0 < |z| < T.

A: Cauchy residue theorem is one of the method to evaluate the integral of analytic functions.…

Q: 2) Find the 3 Taylor pelynomial P,(x) of fix) = Sinx at X = * ½

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Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the Taylor polynomial T3 (x) for f (x) sin x centered at a =

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Q: Vn+ cos n lim Vn +1 1. Evaluate with proof, using the Squeeze Theorem: 2-0

A: To evaluate the below limit using the squeeze theorem. limn→∞n+cosnn+1

Q: Determine the first three nonzero terms in the Taylor Polynomial approximation for y' = cos x + e2x,…

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